Asymptotic Notations in Algorithms

 Asymptotic notations are used in computer science to describe the time complexity of algorithms. Time complexity refers to how much time an algorithm takes to execute as the input size grows. Asymptotic notations provide a way to express the upper and lower bounds of the running time of an algorithm as the input size approaches infinity.

The three most commonly used asymptotic notations are:

1. Big O notation (O): This notation represents the upper bound of the running time of an algorithm. It describes the worst-case scenario for an algorithm, i.e., the maximum time it can take to execute for any input of size n. For example, if the time complexity of an algorithm is O(n), it means that the algorithm takes no more than n steps to execute, where n is the size of the input.

2. Omega notation (Ω): This notation represents the lower bound of the running time of an algorithm. It describes the best-case scenario for an algorithm, i.e., the minimum time it can take to execute for any input of size n. For example, if the time complexity of an algorithm is Ω(n), it means that the algorithm takes at least n steps to execute, where n is the size of the input.

3. Theta notation (Θ): This notation represents both the upper and lower bounds of the running ytime of an algorithm. It describes the tight bound on the running time of an algorithm, i.e., the range of times an algorithm takes to execute for any input of size n. For example, if the time complexity of an algorithm is Θ(n), it means that the algorithm takes between n and k*n steps to execute, where k is some constant factor that does not depend on n.

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Graphical Representation of Asymptotic Notations:-